What is a Reference Angle?

The reference angle is the positive acute angle that can represent an angle of any measure.

The reference angle $$ \text{ must be } < 90^{\circ} $$

In radian measure, the reference angle $$\text{ must be } < \frac{\pi}{2} $$

Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

Rules of Angles and Reference angle

Positive angles go in a counter clockwise direction. Below is a picture of a positive fifty degree angle

Quadrant I

Every positive angle in quadrant I is already acute...so the reference angle is the measure of the angle itself: